0. Hypothesis

 

0.1 Short rational

  • Temperature and enrichment are predicted to have dramatic impacts on food-webs

  • Stability is theoretically predicted to have an U-shape with temperature (Uszko et al. 2017), higher temperature leading to higher stability in “cold” food-webs, and to lower stability in “hot” food-webs

  • Futhermore, metabolic theory predicts that higher trophic level suffer most from high temperature. Metabolic costs increase exponentially with temperature and higher trophic levels have generally higher body mass and then higher basal metabolic cost

  • Enrichment (measured here by DBO), is predicted to decrease stability by increasing the amplitude of population fluctuations (Rosenzweig 1971)

  • Insterestingly, enrichment is predicted to dampens the effect of high temperature by increasing resources thereby decreasing starvation risk due to high temperature (Tabi, Petchey, and Pennekamp 2019)

  • Stream and lakes are really different ecosystems:

    • Stream fishes are highly contrained by stream flow
    • Lakes are highly vertically stratified but offer limited opportunity for dispersal
    • Streams are horizontal stratified and offer opportunity for dispersal
  • Develop hypothesis:

    • about differences between lakes and streams…
    • about the different network metrics

 

0.2 Methods

  • Network metrics: Connectance, Max trophic level, Mean trophic level, number of nodes
  • Environment: Temperature and DBO (to detail)

 

0.3 Statistical ideas

  • Simple linear model:

\(N_i = \alpha + \beta_0F + \beta_1T_i + \beta_2T_iF + \beta_3D_i + \beta_4D_iF + \beta_5D_iT_i \beta_6D_iT_iF+ \epsilon\)

  • With:
    • \(i\): site i
    • \(N_i\): Network metric of site \(i\)
    • \(D\): DBO
    • \(T\): Temperature
    • \(F\): freshwater ecosystem type, lake or stream (logical variable ?)
    • \(\alpha\): intercept
    • \(\beta\): slope
    • \(\beta_2\), \(\beta_4\), \(\beta_5\): slope of simple interaction
      • \(\beta_2\): link between network metrics and temperature change with ecosystem type ?
      • \(\beta_4\): link between network metrics and DBO change with ecosystem type ?
      • \(\beta_5\): link between network metrics and DBO change with temperature ? (hyp enrichment and temperature compensate each other)
    • \(\beta_6\): slope of triple interaction; effect of temperature on the link between network metrics and DBO change with ecosystem type ?
  • Structural Equation Model (one for each ecosystem type ?) (Gibert 2019):

We certainly need to assess the collinearity among network descriptors in the SEM, it may be high, but it was ok in (Danet et al. 2021).

 

1. Temporal and spatial coverage

Due to biological and environmental data availability, the temporal coverage is from 2007 to 2016.
91 sampled lakes and 274 sampled stream stations were considered.

 

2. Environmental variables

Lake
Stream
variable mean sd median min max mean sd median min max
dbo (mg/L) 1.5 0.9 1.3 0.5 5.5 1.6 0.6 1.5 0.6 4.9
temperature (°C) 13.9 1.9 13.6 9.6 18.5 11.3 1.9 11.3 1.8 17.8

 

3. Food web metrics

Lake
Stream
metric mean sd median min max mean sd median min max
connectance 0.1 0.0 0.1 0.1 0.2 0.2 0.0 0.2 0.1 0.2
max trophic level 4.0 0.2 4.0 3.1 4.5 3.8 0.2 3.8 2.9 4.4
mean trophic level 3.3 0.2 3.3 2.2 4.0 3.5 0.3 3.5 2.7 4.2
number of nodes 40.8 10.2 39.0 21.0 67.0 31.4 14.8 30.0 8.0 92.0

 

4. Environmental variables vs. Food web metrics

References

Danet, Alain, Maud Mouchet, Willem Bonnaffé, Elisa Thébault, and Colin Fontaine. 2021. “Species Richness and Food-Web Structure Jointly Drive Community Biomass and Its Temporal Stability in Fish Communities.” Ecology Letters 24 (11): 2364–77. https://doi.org//10.1111/ele.13857.
Gibert, Jean P. 2019. “Temperature Directly and Indirectly Influences Food Web Structure.” Scientific Reports 9 (1): 5312. https://doi.org/10.1038/s41598-019-41783-0.
Rosenzweig, Michael L. 1971. “Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time.” Science 171 (3969): 385–87. https://doi.org/10.1126/science.171.3969.385.
Tabi, Andrea, Owen L. Petchey, and Frank Pennekamp. 2019. “Warming Reduces the Effects of Enrichment on Stability and Functioning Across Levels of Organisation in an Aquatic Microbial Ecosystem.” Edited by Tadashi Fukami. Ecology Letters 22 (7): 1061–71. https://doi.org/10.1111/ele.13262.
Uszko, Wojciech, Sebastian Diehl, Göran Englund, and Priyanga Amarasekare. 2017. “Effects of Warming on Predator-Prey Interactions - a Resource-Based Approach and a Theoretical Synthesis.” Edited by Ulrich Brose. Ecology Letters, March. https://doi.org/10.1111/ele.12755.